Model: Simulating When an Infection Starts to Slow

This model, developed by Palisade consultant José Raúl Castro, uses @RISK to simulate when, after the start of a pandemic, the spread of an infection will start to slow. The assumptions were built using approximate data for the COVID-19 pandemic, and applied to a hypothetical population of 1,000 individuals. The simulation examines 1,000 different scenarios (iterations of a simulation).


The result of the simulation is a distribution showing possible days the infection will reach its turning point and begin to infect fewer people. This just means @RISK displays a range of values as a graph that shows you the probability of different days being the turning point. In our simulation, there was a ~90% chance that the virus will begin to slow between 22 and 29 days into the pandemic, with the 25th day being the most likely.

The main assumptions of this model are the following:

  • The total size of the population is 1,000 people
  • The initial number of infected individuals is 10 people
  • The daily number of people that have contact with an infected person is a random input variable with a minimum value of 3, a most likely value of 4 and a maximum value of 5 (represented by a Pert probability distribution)
  • The probability of getting infected after exposure is 10%
  • Once a person gets infected, the chances of being sent to the hospital vary from a minimum of 10%, a most likely value of 15% and a maximum value of 20% (a Pert distribution). If this does not happen, the individual is sent to his home where he will eventually recover from the disease.
  • The probability that a member of the population dies after hospitalization range from a minimum of 1%, a most likely value of 5% and a maximum of 8% (a Pert distribution).
  • The total recovery period an individual who survives is 14 days, which is considered in the reduction of the number of infected people over time. This period applies to people who safely recover at home and those who went to the hospital.

In order to determine the moment in time where there is a shift in the trend of infection, the model compares two consecutive moving averages of length 3 as displayed in column M. In addition, the model utilizes the RiskCompound function to combine the total number of infected people with the number of people each individual encounters per day (itself a Pert distribution) to arrive at a total number of new people exposed to the virus each day of the pandemic.

You can download the model and change any assumptions you’d like, including the number of iterations @RISK runs. The model updates its graphical progress during simulation, but you can speed it up by turning off the graph, and by enabling the use of multiple CPUs in your computer. You can also add uncertainty to other model inputs, such as the probability of infection after exposure (cell B7) or the recovery period (cell B8).

Download the model